earnings in firm valuation and their value relevance · page 1 of 38 earnings in firm valuation and...

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Earnings in firm valuation and their value relevance

Victoria Clout

UNSW, Sydney, Australia

Michael Falta

University of Otago, New Zealand

Roger J. Willett

University of Tasmania, Australia

Working paper: 23 June 2015

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Abstract

The closely related issues of the role of earnings in equity valuation and the ‘value relevance’

of earnings are investigated through a combined cross-section and time series regression

analysis. Market and earnings data from a sample of 30 long lived, well known US firms is

modelled over the period from 1955 to 2011. The results generally show a decreasing role for

earnings in equity valuation in recent years. The models suggest that the underlying cause of

the decline of the value relevance may be due to earnings management in the majority of the

firms studied.

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1. Introduction

This paper addresses the issue of the place of earnings in equity valuation and the related

question of the ‘value relevance’ of earnings. The value relevance of earnings is broadly

defined in this context as the property of earnings to statistically explain and predict better

than what would be expected by chance and where the direction of cause-and-effect, form

earnings to returns is clear.

To investigate this issue a combination of cross-section and time-series models are

used. The cross-section provides information about changes in the sample over time, while

the time-series capture important dynamic elements of the relationship between market value

and earnings. Unlike most prior research all the models estimated are multiplicative in form.

This form is suggested by overwhelming empirical evidence that the lognormal is generally a

much better approximation than the Gaussian to the distribution of both market value and

earnings in the cross section and over time (Willett, 2015).

The statistical models apply error correction principles to model market returns. A

sample of thirty of the largest, most long-lived US firms is studied using annual data over 57

years from 1955 to 2011. All the firms have 31 December year-ends and make up over 10%

of the value of US corporate equities at any time during the sample period.

The cross-section models show that the response of market value to earnings, gauged

as the statistical significance of the long-run earnings elasticity of market value, has

diminished noticeably since 1978. The time-series models show that only a minority of

eleven of the firms in the sample exhibit any evidence of a systematic relation of returns with

earnings and in only four of these firms is the relationship strong. In the remainder, the

majority, the lack of such a relationship is accompanied by a statistically significant mean-

reversionary property in the time series of earnings. Further investigation shows that errors in

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earnings measurement are likely caused by earnings management in the firms concerned.

This in turn is adduced as a probable cause of market disbelief in published earnings data in

recent years, leading to the reduced value relevance of earnings.

The results supporting these findings and a discussion of these are contained in

Sections 4 and 5 of the paper respectively. The next Section briefly reviews the literature

while Section 3 explains the theory, method and data underlying the findings. Section 6

concludes.

2. Prior research

In the literature, the value relevance of earnings has two common interpretations. In much

cross-section research it simply refers to the existence of a significant coefficient on the

earnings variable in a regression of market value or returns on regressors including the

earnings variable (e.g. Barth et al., 1999). A different but largely consistent interpretation of

value relevance of earnings is more closely related to research using time series modelling,

whereby value relevance is related to the ability of earnings to explain and predict the

behaviour of market value and returns (e.g. Qi et al., 2000).

Empirical studies put forth contrasting explanations about the hypothesised causes,

changes and the direction of changes in the value relevance of earnings. The influential paper

by Collins et al. (1997) argues that the advent of information technology oriented economies,

effects from non-recurring items, negative earnings, and the growing number of small firms

included in Compustat samples used for research contribute to the appearance of growing

value-relevance of earnings and book values. Keener (2011) extends the Collins et al. study

through a longer data series and concurs with the original findings, as do Asthana and Chen

(2012) who focus on particular industry sectors.

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Some studies find that increases and decreases in value relevance of earnings depends

on country and, institutional and legal environment (e.g., Hail 2013). D’Mello and Gruskin

(2013) suggest the direction of change depends on investor sentiment and behavioural factors

which may swing according to macroeconomic cycles and events. In related research Barth et

al. (1999) connect the behaviour of the PE ratio to time patterns of earnings while Cheng

(2005) finds associations between earnings ratios and changes in various industry

characteristics over time.

Generally however, decreased value relevance of earnings has been suggested to be

due to increased earnings volatility (Dichev and Tang, 2008), an increase in restatements

(Wilson, 2008), a change in stickiness and distributional properties of earnings (Balachandran

and Mohanram, 2011), or driven by changes in market-forces and innovation (Lev and

Zarowin, 1999). Lim and Park (2011) following Francis and Schipper (1999) find that the

temporal decline of earnings relevance is due to market noise.

The valuation models most widely used in empirical studies of capital markets

research to establish value relevance are the residual income models based on Ohlson (1995)

and Feltham and Ohlson (1995). To date there have been many empirical investigations of

the Ohlson model using a cross-sectional approach (e.g., Abarbanell and Bernard, 1995;

Dechow et al., 1999; Francis et al., 2000; Frankel and Lee, 1998; Penman and Sougiannis,

1998).

However, the Ohlson model has been challenged on the linearity assumption

(Davidson et al., 2012), the reliability of forecasted individual accounting fundamentals to

explain market value (Penman and Reggiani, 2013) and the reliability of forecasted discount

rates (Penman 2010). In general, the nature of the research question about temporal change

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suggests a more dynamic research setup (Callen and Morel, 2000; Ely and Robinson, 1997;

and Bartholdy et al., 2003).

Campbell and Shiller, 1988; Lee et al., 1999; Ritter and Warr, 2002, studied the co-

movement of stock prices and fundamental values, considering temporary deviations which

can be caused by bubbles, mispricing, conservatism or optimism in the market. Prior studies

have investigated this ‘co-movement’ through the technique of co-integration (Collins et al.,

1994; Weiss et al. 2008; Qi et al., 2000). Qi et al. (2000), for example, investigated the

existence of co-integration at the firm level between market values and earnings, using an

Ohlson model approach, and found evidence of only weak co-integration.

The many potential factors and approaches discussed above suggest disagreement

about the direction of change in value relevance, are perhaps driven by method and sample

selection rather than representative of an underlying economic reality (e.g. Lev and Zarowin,

1999, versus Collins et al., 1997). Willett (2015) finds that the distributional properties of

earnings (and book values) for Compustat firms are strongly lognormal, whether the data are

cross-sectional, time series or pooled. We therefore use as a starting point Falta and Willett

(2013) who propose a multiplicative theory of the market-accounting relation based on the

exponential growth characteristics observed in the fundamental accounting variables which

aligns well with the observed distributional properties. Their theory is explained in more

detail below.

Theory, method and data

Theory

The analysis in this paper is based only on the broad theory that the market obeys a partial

adjustment mechanism in valuing shares. For whatever reason, rational or irrational, the

market values each firm using a multitude of information sources, among these, possibly,

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accounting data. If the basis of such valuation, as a function of the various explanatory

variables, remains stable over time as the explanatory variables change, it must mean that

market participants are adjusting share values to these changes by their buying and selling

activities. Since knowledge and market behavior is subject to error, how errors are corrected

can inform us as to the relevance of a particular information source, such as accounting

earnings, for market participants in the valuation of shares. This is the basis of the approach

adopted in this paper to investigate the value relevance of earnings.

We assume that the pure time series of market value at time , for each firm , , is

approximately distributed as a lognormal random variable and that it follows a geometric

Markov process,

( 1 )

in which and are constant over time but vary between firms and is lognormal. This

form for the process governing market value is consistent with theories of share value in

finance (e.g. Black & Scholes, 1973). It is known there are problems with the tail

characteristics of the returns distribution, so that the assumption that it is lognormal is

ultimately not an accurate description of the distribution of market value. However, we are

interested in its relative accuracy as a better approximation to the true generating process,

compared to models generally adopted in prior research, as described in the previous Section.

This can be assessed by examining diagnostic statistics.

Firm market value is commonly held to follow a random walk, in which case .

Proportional returns, ⁄ , are then unpredictable since, ⁄ . When

, however, an element of predictability in proportional returns is provided by

knowledge of . Letting

and

, we see that,

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(

)

( 2 )

In this case, proportional returns ‘mean revert’ to the function of the long-run exponential

growth rate in the denominator on the RHS of (2).

The ‘value relevance’ of earnings for market value is indicated by the extent to which

market value is explained and predicted by including a function of earnings, in (1), i.e.,

( ) ( 3 )

Generally, this is indicated by the extent to which and, more specifically, by the

ability of the model in (3) to improve prediction of the next period’s direction of abnormal

returns relative to (1). Following Falta and Willett (2013) the functions of explanatory

variables we consider are of the form,

( )

( 4 )

Substituting (4) into (3) we can derive an autoregressive distributed lag (ADL) model

between market value and earnings, i.e.

( 5)

Algebraically transforming (5) into its returns counterpart, corresponding to (2), we

get the form:

(

)

(

( )

)

(6)

Here ( ) ⁄ is the long-run earnings elasticity of market value. The terms in

the first set of parentheses on the RHS of (6) reflect the short-run impact of changes in

earnings on proportional market returns, i.e. the short-run earnings elasticity of returns. The

term shows the strength of the error correction effect on proportional market

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returns. The denominator in the second set of parentheses is interpreted as the long-run or

fundamental market value based upon earnings, so that the ‘error correction’ coefficient is an

indicator of the speed of adjustment measuring the strength of the mean reversion of market

value to its fundamental value. The difference between the numerator and denominator

reflects an imbalance, ‘error’, in the fundamentals that is partially ‘corrected’ in successive

periods of time, after accounting for any short term effect contained in .

In summary, the underlying theory about the long-run market behavior on which these

models are based is one of partial adjustment by the market to differences between observed

market value and what was expected based upon the value of earnings. In the next Section,

we assess the strength of the returns-earnings relationship in the sample firms.

Method

Models of the form shown in Expressions (5) and (6) cannot, in general, be validly and

reliably estimated by cross-sectional, or the usually implemented panel, methods of analysis.

Pesaran & Smith (1995) recommend separately estimating the time series model in each

individual case in the panel of data (firms in this instance) and then explicitly averaging the

individual estimated coefficients to provide cross section estimates of the parameters of

interest for the sample as a whole. This is the approach we take in the time series modelling.

In the cross-section we estimate the long-run ‘levels’ where market values are represented by

a simple, static regression model without any lags. This is shown to be a reliable way to

estimate the long-run parameters of processes of the type described by (5) by Madsen (2005)

and Pesaran and Smith (1995).

We use ordinary least squares, which is the technique assumed by Pesaran & Smith,

by taking logs of the data and estimating the models1:

(7)

1 Negative earnings are dealt with either by replacing them with a function of the hyperbolic sine transformation

or by their absolute values (see Willett, 2015).

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and,

∑ ( )

(8)

A conditional error correction approach based on the single equation, Engle and Granger

two-step method is used to estimate the ADL form of the models and then, in the second

stage, the ECM form. In principle, it is possible to derive ECM’s of the form of (6) from the

corresponding ADL form in (5) algebraically but the ECM form is estimated separately with

PcGive to provide various diagnostic and inferential statistics (Doornik and Hendry, 2013).

We use the diagnostic tests shown in Table 1 to check the statistical assumptions of the

multiplicative models against the corresponding additive models2.

[INSERT TABLE 1 ABOUT HERE]

The Augmented Dickey-Fuller ( ) tests used to test for co-integration between market

values and earnings are described in Table 2. The variables are judged to be co-integrated if

the average test statistic across models including a constant or trend term, both or neither,

with up to two lags on the error term, implies an average significance level of less than 10%.

Predictability of models is judged by counting the number of times the direction of change in

returns is correctly predicted in conditional, one-period-ahead forecasts by the model in ten

year hold-out periods. A random walk, in the absence of drift, would predict the direction of

change, or ‘turning points’ 50% of the time. We use a higher percentage, 62.27%, as a

benchmark to compare the predictive ability of the accounting variables. This is the number

of times a simple time series model of market value correctly predicts turning points one

period ahead and makes an allowance for drift in this sample of firms. The predictability

statistic, which we dub for ‘Number of Turning-Points (correctly) Predicted’ is also

described in Table 2. It is used to assess the strength of the value relevance of earnings and in

the simple Granger causality tests reported in the next Section.

2 All additive models of the relations estimated show clearly higher mis-specification compared to the multiplicative models and they are not reported. Details of these tests are available on request from the authors

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[INSERT TABLE 2 ABOUT HERE]

Data

Our data set consists of the variables shown in Table 3 for the firms listed in Table 4 from

1955 to 2011. Firm market value is calculated as actual shares outstanding at the balance

sheet date (all firms have 31 December year ends) multiplied by actual closing share price at

the same date. Earnings are the values stated in the financial statements of the relevant firms,

as per Compustat. The firms in the sample represent nearly all those listed on Compustat that

have continuous data for earnings, over the sample period. They are therefore a selected, not

a random, sample and represent survivors. However, they also represent between 10% and

15% of the total value of US listed equities over the sample period and are therefore

important in that respect.

[INSERT TABLES 3 AND 4 ABOUT HERE]

3. Results

Summary statistics

Table 5 provides summary statistics of averages for the firms in the sample covering the

period used for estimation from 1955 to 2001. Log transforming the data alleviates both

skewness and kurtosis of the market value data but this effect is less evident in the earnings

data, both in levels and in changes. The market to book ratio across the sample is about 3 and

the market to earnings ratio (i.e. the price earnings ratio) is about 18. The growth in market

value, book value and earnings is about the same, around 8% - 9% when the data is logged,

as the distributional properties of the raw data suggest it should be.

[TABLE 5 ABOUT HERE]

Cross-section evidence of changes in the value relevance of earnings over time

Table 6 shows coefficient estimates and inferential statistics for cross section models of

market value regressed on earnings. In theory, if the model variables are co-integrated, and

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the sample sizes are large, well specified models of this type should recover unbiased

estimates of the relevant parameters, i.e. long run estimates of the response of market value

with respect to earnings.

[TABLE6 ABOUT HERE]

Table 6 shows the firm average, long run earnings elasticity of market value tracking

downwards over the sample period, accompanied by increasing volatility in the estimates.

Figure 1 displays the extent of the volatility graphically. Panel A shows the time series of the

price-earnings ( ) ratio, Panel B the estimated yearly earnings elasticity of market value,

Panel C the theoretical, linearized estimate of the ratio, ,3 and Panel D the ratio of the

ratio to .

[FIGURE 1 ABOUT HERE]

The Table and the Figures all show in their different ways the increasing volatility and

declining average yearly ratio for this sample of firms over a long period of time. Up until

1978 earnings elasticity averaged 1, taking one year with another. From 1979 the average

elasticity averaged only 47%. The ratio fell from an average 20.18 in the 24 years to 1978

to 13.23 over the period 1979 to 2011. The average value of also fell from 16.28 to 12.61

during the same periods. The average ratio of the ratio to was 1.24 from 1955 to 1978

and 1.08 from 1979 to 2011. The Figures show an increase in the volatility of all these time

series after 1987.

The lowering of the premium on earnings evident from the falling ratio at a time

of increased volatility may possibly be explained by low interest regimes. The falling

elasticities, however, show a significant fall in the market response to information relating to

3 This is defined as

, where

. It is the marginal ratio at the average level of

earnings divided by its long-run elasticity (see Clout and Willett, 2015)

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earnings over the latter part of the time period. Taken together these two patterns suggest

falling value relevance of earnings or, its statistical representative in time series analysis, a

lessening of the co-integration between market value and earnings.

With the type of data available and given the coefficient patterns displayed it is

unlikely that cross-section analysis will provide a reliable indication of speed of adjustment

metrics and short run elasticities, so we turn our attention next to time series modelling.

Time series evidence regarding the value relevance of earnings

Table 7 displays the same variable fields for the firms in the sample as does Table 6 for the

years in the sample. The coefficients in this Table are long-run estimates only, based on the

static regression . This is likely to give biased estimates of the true long-run

parameters but has the advantage of not returning as sensitive estimates of the long-run

ratio as does its ADL counterpart.

[TABLE7 ABOUT HERE]

The time series estimates for some of the firms show marked multiplicative, non-

linearity and in these cases the long-run estimate of the ratio, , is noticeably different

from it observed value. This could be due to the model not working well in that case or it

could be due to the long-run and short-run elasticities for the firm concerned being

significantly different from one another. However, inspection of the Table shows that a

number of the highly non-linear models are associated with low or insignificant earnings

elasticity estimates, or both of these. This indicates weak co-integration between market

value and earnings. About half of the firm sample show quite close correspondence between

the expected theoretical long-run ratios represented by and the observed average

ratios, .

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To investigate the extent of co-integration between market values and earnings in the

sample of firms, the long-run estimates embodied in the time series data in Table 7 are used

to form error correction variables for each firm. These are tested for stationarity and

proportional changes in market values (‘returns’) are regressed against these and proportional

changes in earnings, corresponding to the model described in (6).

The resulting estimates and inferential statistics are shown in Table 8. While 25 out of

the 30 firms show some signs of co-integration by the ADF tests, these are quite generously

interpreted (see Section 4). More noticeable is the low number of firms showing a lack of

significance in the short-run and error correction coefficient estimates at 5% significance

levels. Even at 80% confidence levels most of the coefficient estimates are not significant

and the statistic is also low in most of the models4.

[TABLE8 ABOUT HERE]

The results of these tests and the preceding ones therefore indicate evidence of weak

co-integration in some of the firms between market value and earnings but a deal of variation

between the firms’ parameter estimates. Recursive graphics suggest the differences between

the estimates are not a transitory phenomenon, indicating considerable heterogeneity between

firms. Overall the estimated models suggest the average value relevance of earnings for

market value for these firms in this period was low, based on the ability of earnings to explain

or predict returns.

In the next sub-Section we consider if market value shows any ability to predict future

earnings, i.e. if there appears to be a reverse causation effect.

Causality tests - Does market value lead earnings?

The models now considered reverse the roles of the variables with earnings being the

regressand and market value being the regressor. No short-run variable is entered in these

4 Forecast and diagnostic tests not reported do not indicate significant model mis-specification.

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models as the interest is in the predictive ability of the error correction term for the sign on

next period’s earnings growth. These are simple versions of the ‘Granger causality’ test. The

results of estimating this model are shown in Table 9. It is noticeable that the significance of

the average error correction term is much higher than in Table 8 and that a far larger number

of firms produce a statistically significant result. These estimates are possibly not very

reliable as the models are generally not well-specified. However, as the role of these models

is to test predictability this is not particularly important. The key statistic is shown in the

metric which shows an apparent ability to predict one period ahead in the ten year hold-out

period of 7.60.

[TABLE 9 ABOUT HERE]

The ability of the error correction part of the model to predict in this way is well

beyond a chance finding and appears to indicate that market value leads earnings. However,

the models whose estimates are displayed in Table 10 suggest that the ability of market value

to predict earnings is due to a mean-reversionary element in the earnings series itself. Table

10 contains estimates relating to a simple earnings time series model.

[TABLE10 ABOUT HERE]

The correlation between the error correction terms in the causality tests and those in

the time series of earnings models is 91%. The correlation between the former and the

parameter estimates in the ‘earnings relevance’ models in Table 7 is a negative 41%. This

suggests the weak value relevance exhibited by the firms’ earnings for returns is connected in

some way to their mean-reversionary property.

4. Discussion

The apparent ability of returns to predict earnings and the mean reversion evident in earnings

could be due to a number of causes other than earnings management, including: ‘forward

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looking’ information contained in market values; firms being well managed; or firms

following a path dictated by equilibrium forces, such as industry effects in the long-run.

However, the evidence reported in the previous Section and other information contained in

this sample of firm data suggest earnings management is the most likely explanation for the

decline in the value relevance of earnings.

The cross-section evidence shows that the market’s perception of the value relevance

of earnings information has declined since 1978. Before that date the earning elasticity of

market value averaged 100%, whereas after that date it approached that level again only in

1987-89, falling to 12%-13% in 2001-2 and 16% in 2008. The average long-run elasticity for

the period after 1978 was only 47%, as already noted.

The Tables and Figure relating to the time series of the cross-section estimates also

show increasing volatility in the earnings elasticity of market value and the ratio after

1978. From the estimate of it can be seen more clearly that years of low average long-run

elasticity were associated with generally lower ratios. Overall the valuation of earnings

appears to have fallen as well as its value relevance.

The average cross-section observed ratio over the entire period was 16

compared to 18 for the same ratio computed for each firm’s time-series data and averaged

across the firms. is lower than the ratio in the cross-section data and less volatile but is

greater than the ratio in the time-series data and more volatile. Due to the strongly

trending nature of the time-series data, the cross-section estimates are likely to be more

representative of underlying averages.

The interesting point about the time-series data in Table 7, connecting it to the cross-

section model estimates suggesting weak value relevance for earnings, is the marginal

influence on market value of earnings in most of the firm error correction models. In a strong

ECM of returns on earnings one would like to see a long-run earnings elasticity of market

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value close to 100%, to justify its characterization as being ‘sufficient’ to explain movements

in market value, a value of similar to the relevant firm’s ratio, a large negative error

correction term (ECT) less than 1 in magnitude, with all of the model coefficients being

statistically significant at levels not less than 5%. Only four firms in the sample come close

to satisfying these criteria. Another seven firms have long-run earnings elasticities close to

100% but in these cases the presence of the ECT is marginal at best. The models of these

firms tend to have either a low short-run earnings elasticity of returns or a low value ECT, or

both. The remaining 19 firms display low short-run responses of returns to earnings changes,

low long-run earnings elasticities of market value and tiny error correction effects. Thus all

models indicate either a minor immediate response of returns to changes in earnings or a very

slow correction of market value to any long-run relation it has with the level of earnings. The

causality tests and highly correlated mean-reversion properties of the earnings series reported

in Tables 9 and 10 are consistent with the assessment of a weak or no co-integration effect

between returns and earnings in the firms in the sample.

To see why mean-reversion properties in earnings time series may be related to

earnings management, consider that the rules of accounting measurement require that,

(9)

where , and are respectively the changes in retained earnings, undistributed

earnings and errors in measuring earnings for firm during period 5. Retained earnings, ,

reflect an accumulation of evidence concerning the aggregated value of a firm’s activities

over a long period of time. The metric of therefore represents a long-term indicator of

increments in firm wealth and published earnings should on average, over time, agree

5 This assumes there is no error in measuring dividends.

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with it. However, as can be seen from Figure 2, after 1978 is upwardly biased compared

to .

[FIGURE 2 ABOUT HERE]

Figure 2 shows the average value of the error in earnings, , compared to changes in

retained earnings, , for all the firms in the sample for each year from 1960 through to

2011. The negative sign indicates that published earnings overstate the earnings element that

is ultimately reflected in retained earnings. In addition the volatility of the error in earnings

noticeably increases in the period after 1978, suggesting a link to the decreasing importance

of earnings in valuing shares evident from the cross-section evidence in Table 6. The graph in

Figure 2 shows a pattern typical in the individual time series of the error variable of nearly all

the firms in the sample.

The nature of the dynamic relationship between and is revealed by the

estimates from the error correction model of the former based on the latter in Table 11. In

high quality earnings measurement based on clean surplus principles, one would expect to see

models with an error correction coefficient and short ( and long-run error

elasticities ( ) with respect to retained earnings close to 1. This would show that the

value of retained earnings reflects undistributed earnings for each year, with any errors being

corrected quickly. The parameter estimates in Table 11show a great deal of heterogeneity

between firms with an average error correction parameter estimate of 0.76, a short run

elasticity of response of 0.5 and a long run elasticity of response of 0.66. This suggests a

marked difference in the firm sample between earnings generating ability as shown in income

statements and the picture of accumulated income over time as portrayed in balance sheets.

[TABLE11 ABOUT HERE]

Conclusion

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In this paper, using models with multiplicative forms, argued to be more reliable than those

usually adopted for the purpose of investigating the value relevance of earnings, cross-section

evidence of declining earnings value relevance for returns is found in a sample of large, long-

lived US firms. Time-series analysis using error correction principles produces evidence of a

low level of co-integration between market value and earnings. The ability of market value

to predict earnings, mean-reverting properties of earnings and the behaviour of errors in

earnings measurement suggest the weak co-integration may be due to earnings management.

This is therefore conjectured to be a major cause of the apparent lack of value relevance of

earnings in these firms in the later periods of the sample data. On average, across the firms

studied, market participants do not believe the earnings numbers reported in financial

statements as factual but rather as possibly optimistic forecasts of what firm managers would

like their earnings to be.

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Tables

of 38

Table 1: Diagnostic tests used to check model validity

Test (with

abbreviation) Reference Comments

Autoregressive

conditional

heteroscedasticity

(ARCH)

Engle (1982)

-test of the null of no dependence of the

current squared error on previous values of

the squared error from the model. Doornik &

Hendry (2013: 277-8)

Autocorrelation

(AR) Harvey (1990)

-test form for unconditional autocorrelation.

The null hypothesis is of no autocorrelation

of residuals. Doornik & Hendry (2013: 275).

Normality (DH) Doornik and

Hansen (1994)

2-test. Null hypothesis is normality of

residuals. Doornik & Hendry (2013: 276).

Heteroscedasticity

(Hetero)

White (1980)

-test of null of unconditional

heteroscedasticity against alternative that the

variance of the error process depends upon

squares of the regressors as well as the

regressors themselves. Doornik & Hendry

(2013: 277).

Regression

specification test

(RESET)

Ramsey (1969)

-test of null of correct specification against

alternative that squares of estimates of the

dependent have been omitted (as per Doornik

& Hendry (2013: 278).

Parameter

constancy

(Chow, 1960) see

Doornik and

Hendry (2013: 253).

Chow test of parameter constancy

Accuracy of

forecasts

(Harvey and Collier,

1977) see Doornik

and Hendry (2013:

253).

CUSUM test for zero mean of one-period-

ahead forecasts

of 38

Table 2: Unit root used to test for co-integration and the NTP statistic

Test statistic Source Description

Unit root tests Dickey and Fuller (1981)

The appearance of a significant

statistic based on a non-standard

distribution, in ADF tests

including no constant, a constant

and a constant plus trend. The null

is non-stationarity. Doornik &

Hendry (2013: 238-9).

NTP The number of occasions in ten

hold periods that the error

correction model correctly

forecasts the change in the

direction of proportional returns

one-period ahead.

of 38

Table 3: Variables used in models 1

2

Data Sources

Earnings (E),

dividends (D) and

book value of net

assets (B)

As defined by Compustat annual data item numbers A172, A21 and A60 respectively.

Sources: Compustat tapes: 1955-2011.

Market value (M) Defined as share price at fiscal year-end (A199) multiplied by the number of shares

outstanding. Sources: Compustat 1955 – 2011.

3

of 38

Table 4: Details of firms in sample 4

5

Company Ticker

Fama and French

Industry sectors

Market Cap.

In 1999

Millions US$

Percentage

of Total

US

Market

Cap.

Abbott ABT Health Care 56176.16 0.34%

Altira MO Tobacco Products 53785.94 0.32%

Beam BEAM Beer & Liquor 5397.22 0.03%

Bristol-Myers Squibb BMY Health Care 127142.99 0.76%

Chevron CVX Petroleum and

Natural Gas

56855.97 0.34%

Coca Cola CCE Candy & Soda 143969.24 0.87%

Colgate-Palmolive CL Consumer Goods 37626.10 0.23%

Cooper Industries CTB Automobiles &

Trucks

3809.21 0.02%

Corning GLW Construction

Materials

33549.54 0.18%

Crane CR Construction

Materials

1248.19 0.01%

Curtiss-Wright CW Machinery 370.23 0.00%

CVS Caremark CVS Retail 15630.84 0.09%

Du Pont DD Chemicals 68847.94 0.41%

Eaton ETN Machinery 5374.25 0.03%

Exxon XOM Petroleum and

Natural Gas

280115.81 1.68%

General Electric GE Electrical equipment 508329.45 3.06%

Goodyear GT Automobile and

Trucks

4387.15 0.03%

Honeywell HON Automobile and

Trucks

45869.23 0.28%

IBM IBM Information

Technology

192472.30 1.16%

Ingersoll IR Machinery 8982.29 0.05%

International Paper IP Business Supplies 23331.26 0.14%

Johnson & Johnson JNJ Health Care 129587.94 0.78%

McGraw Hill MHFI Business Services 12060.57 0.07%

Merck & Co MRK Health Care 156484.86 0.94%

Motorola MSI Electronic Equipment 90234.80 0.54%

Olin OLN Chemicals 892.79 0.01%

Pfizer PFE Pharmaceutical

Products

124787.06 0.75%

Raytheon RTN Electronic Equipment 8998.31 0.05%

Textron TXT Aircraft 11273.22 0.07%

United Technologies UTX Aircraft 30845.49 0.19%

of 38

Table 5: Summary data

Pooled data N Mean Std. Error Skewness Kurtosis

Market value 1410 14647.42 1036.53 6.15 52.24

Book value 1410 3919.71 199.55 3.96 20.89

Earnings 1410 707.04 44.02 3.70 22.83

Change in market value 1380 1565.84 307.92 5.65 85.90

Change in book value 1380 274.11 30.60 5.27 91.80

Change in earnings 1380 54.56 19.08 2.22 99.57

Log market value 1410 7.86 0.05 0.15 -0.48

Log book value 1410 7.04 0.04 0.02 -0.56

Log earnings 1410 4.75 0.07 -2.20 8.37

Change in log market value 1380 0.09 0.01 -0.31 2.53

Change in log book value 1380 0.08 0.00 -0.14 18.49

Change in log earnings 1380 0.01 0.07 -0.78 22.01

Market to book ratio 1410 3.07 0.08 3.54 21.83

Earnings to book ratio 1410 0.16 0.00 -0.10 22.01

Market to earnings ratio 1410 17.86 1.12 7.96 245.95

Earning to lagged book value 1380 0.18 0.00 0.28 4.70

Log of earnings to lagged book value 1336 -1.82 0.02 -1.85 9.96

Growth in market value 1380 1.14 0.01 1.50 5.96

Growth in book value 1380 1.09 0.00 6.51 120.64

Growth in earnings 1380 1.15 0.09 17.84 467.11

Log growth in market value 1380 0.09 0.01 -0.31 2.53

Log of growth in book value 1380 0.08 0.00 -0.14 18.49

Log of growth in earnings 1313 0.09 0.01 -0.29 24.08

of 38

Table 6: Cross section estimates of long-run earnings elasticities of market value and

price earnings ratio based on

Firm Period Average earnings PE ratio ( ⁄

1955 2.22 1.11 0.96 74.22 15.02 14.14 0.94

1956 2.39 1.07 0.92 78.34 14.60 15.24 1.04

1957 1.92 1.15 0.90 81.92 13.21 13.05 0.99

1958 2.67 1.08 0.90 69.70 20.43 21.38 1.05

1959 2.52 1.11 0.91 79.45 20.20 20.16 1.00

1960 2.70 1.07 0.88 77.16 20.18 21.64 1.07

1961 4.08 0.76 0.75 84.11 20.12 23.38 1.16

1962 2.62 1.08 0.94 92.61 19.51 19.34 0.99

1963 3.21 0.95 0.87 103.62 19.41 51.01 2.63

1964 2.40 1.13 0.93 113.64 20.77 19.90 0.96

1965 2.62 1.09 0.91 123.66 21.53 21.83 1.01

1966 2.30 1.11 0.86 132.59 17.14 17.97 1.05

1967 2.89 1.03 0.86 141.26 21.21 23.24 1.10

1968 3.11 0.98 0.85 156.28 20.16 23.08 1.14

1969 2.55 1.07 0.82 151.96 18.19 20.49 1.13

1970 4.71 0.61 0.66 160.81 15.07 42.85 2.84

1971 5.43 0.47 0.53 178.23 14.40 24.63 1.71

1972 5.65 0.44 0.43 203.45 14.16 22.83 1.61

1973 1.81 1.14 0.84 278.09 13.71 14.75 1.08

1974 1.53 1.10 0.80 321.69 8.38 9.48 1.13

1975 2.09 1.07 0.84 295.79 11.99 13.00 1.08

1976 2.00 1.09 0.93 350.23 12.46 12.30 0.99

1977 1.78 1.08 0.93 385.31 9.74 9.69 0.99

1978 1.67 1.09 0.94 443.08 9.05 8.95 0.99

1979 3.07 0.83 0.75 553.91 7.29 12.30 1.69

1980 2.62 0.94 0.92 653.76 9.02 10.11 1.12

1981 2.15 0.98 0.85 702.23 7.49 8.41 1.12

1982 6.49 0.30 0.44 621.10 7.24 8.59 1.19

1983 6.84 0.27 0.48 720.86 7.80 12.22 1.57

1984 3.64 0.79 0.91 837.76 9.46 14.08 1.49

1985 7.54 0.19 0.31 789.65 8.54 12.99 1.52

1986 3.09 0.95 0.88 788.75 15.47 18.39 1.19

1987 2.66 0.97 0.88 922.23 11.89 13.49 1.14

1988 2.20 1.03 0.97 1072.51 11.36 11.42 1.00

1989 2.87 0.97 0.82 986.39 14.46 18.20 1.26

1990 6.18 0.44 0.51 1229.66 9.33 11.86 1.27

1991 8.76 0.09 0.06 763.39 15.58 17.55 1.13

1992 9.07 0.07 0.07 531.22 25.49 -1.27 -0.05

1993 8.54 0.15 0.20 728.01 19.02 14.50 0.76

1994 6.81 0.39 0.40 1395.35 11.25 8.25 0.73

1995 8.25 0.22 0.27 1612.09 11.83 13.48 1.14

1996 3.49 0.93 0.88 1915.43 19.65 24.36 1.24

1997 8.11 0.30 0.28 2076.20 15.27 29.56 1.94

1998 8.74 0.22 0.13 2053.82 15.78 25.60 1.62

1999 8.04 0.32 0.32 2544.51 15.60 31.49 2.02

2000 7.56 0.41 0.42 2970.95 16.51 34.70 2.10

2001 9.60 0.12 0.17 2583.86 14.79 4.97 0.34

2002 9.58 0.13 0.29 2332.68 17.30 0.50 0.03

2003 8.64 0.26 0.46 3299.06 13.61 19.58 1.44

2004 9.13 0.19 0.28 4052.06 10.80 -1.84 -0.17

2005 3.47 0.92 0.93 4681.05 16.30 19.46 1.19

2006 7.95 0.34 0.45 5551.56 9.71 16.78 1.73

2007 8.92 0.24 0.40 5477.20 10.57 -15.86 -1.50

2008 9.00 0.16 0.29 5522.29 5.78 8.34 1.44

2009 8.84 0.21 0.34 4494.85 9.14 -3.56 -0.39

2010 7.80 0.36 0.51 4903.75 10.23 21.12 2.06

2011 3.45 0.90 0.90 5774.07 12.73 16.97 1.33

Average 4.91 0.69 0.65 1391.57 14.16 16.16 1.15

St. Dev. 2.80 0.39 0.29 3570.33 4.59 10.60 0.67

St. Error 0.37 0.05 0.04 477.10 0.61 1.42 0.09

LCL 4.18 0.59 0.57

12.95 13.38 0.97

UCL 5.64 0.79 0.72

15.36 18.94 1.32

Notes: ̅

. This is the long-run elasticity linearized with respect to average earnings.

LCL is ‘lower critical limit’ for a z test based on a random sample of 57. UCL is ‘upper critical limit’ based on the same sample.

of 38

Table 7: Time series estimates of long-run earnings elasticities of market value and

price earnings ratio based on )

Firm

Average

earnings

PE ratio

( ⁄

Abbott 2.93 1.01 0.98 1127.98 20.36 20.86 1.02

Altira 2.54 1.00 0.98 1371.31 12.60 13.21 1.05

Beam 7.43 0.09 0.03 1836.78 1.81 10.30 5.70

Bristol 3.16 0.97 0.95 488.49 19.07 22.12 1.16

Chevron 3.17 0.91 0.82 167.52 14.74 15.10 1.02

Coca Cola 3.10 1.01 0.94 252.89 23.04 26.61 1.15

Colgate 2.35 1.10 0.92 1352.76 21.47 20.13 0.94

Cooper 5.03 0.44 0.30 242.01 7.03 7.46 1.06

Corning 8.03 0.01 -0.02 5005.73 0.67 4.30 6.46

Crane 5.72 0.07 0.01 126.15 3.45 9.77 2.83

Curtiss 4.95 0.23 0.25 221.30 2.25 11.09 4.94

CVS 4.75 0.59 0.49 3814.35 3.85 21.79 5.67

Du Pont 9.60 0.02 -0.01 235.39 68.79 17.05 0.25

Eaton 5.92 0.30 0.23 2539.24 1.48 10.74 7.24

Exxon 2.75 0.97 0.90 2070.87 12.33 13.17 1.07

General Electric 3.34 0.95 0.92 257.62 21.02 21.32 1.01

Goodyear 7.69 0.01 -0.01 2284.94 1.04 14.34 13.83

Honeywell 8.09 0.05 0.00 398.33 10.92 9.70 0.89

IBM 10.05 0.10 0.12 207.86 187.20 25.06 0.13

Ingersol 7.28 0.06 0.01 925.01 2.39 13.23 5.53

International Paper 8.53 -0.06 0.03 544.15 6.50 21.04 3.24

Johnson 3.44 0.95 0.97 306.42 23.32 26.47 1.13

McGraw Hill 3.17 0.95 0.85 8664.90 14.67 27.25 1.86

Merck 3.59 0.93 0.95 3631.86 19.96 25.20 1.26

Motorola 8.07 0.03 -0.01 31.05 111.82 22.22 0.20

Olin 6.62 0.01 -0.02 228.47 3.38 25.81 7.63

Pfizer 2.89 1.02 0.96 482.86 20.78 23.35 1.12

Raytheon 6.35 0.29 0.20 2830.06 1.94 34.20 17.59

Textron 6.64 0.14 0.05 58.94 23.19 11.13 0.48

United Technologies 6.62 0.30 0.26 41.79 55.06 11.87 0.22

Average 5.46 0.48 0.43 1391.57 23.87 17.86 3.26

SD 2.34 0.44 0.43 1897.56 38.66 7.28 4.12

SE 0.43 0.08 0.08 352.37 7.18 1.35 0.76

LCL 4.61 0.32 0.28 700.93 9.80 15.21 1.76

UCL 6.31 0.64 0.59 2082.21 37.94 20.51 4.75

Notes: ̅

. This is the long-run elasticity linearized with respect to average earnings.

LCL is ‘lower critical limit’ for a z test based on a random sample of 57. UCL is ‘upper critical limit’ based on the same sample.

* Not significant

of 38

Table 8: Coefficient estimates and inferential statistics for the error correction model:

(

)

(

)

t-Prob. t-Prob.

Abbott 0.17 0.31 -0.29 0.01 0.17

Altira 0.20 0.37 -0.48 0.00 0.24

Beam 0.01 0.33 -0.03 0.33 0.00

Bristol 0.32 0.22 -0.15 0.09 0.03

Chevron -0.05 0.47 -0.02 0.75 -0.02

Coca Cola 0.46 0.05 -0.14 0.07 0.11

Colgate 0.09 0.26 -0.07 0.43 -0.01

Cooper 0.03 0.08 -0.07 0.05 0.08

Corning 0.05 0.00 -0.03 0.61 0.20

Crane 0.03 0.27 -0.03 0.48 -0.01

Curtiss 0.04 0.13 -0.43 0.00 0.16

CVS 0.02 0.37 -0.02 0.64 -0.03

Du Pont 0.00 0.82 -0.02 0.66 -0.04

Eaton 0.02 0.19 0.04 0.55 0.00

Exxon 0.11 0.41 -0.02 0.74 -0.03

General Electric 0.34 0.07 -0.09 0.23 0.06

Goodyear 0.04 0.00 -0.15 0.04 0.21

Honeywell -0.03 0.02 0.03 0.53 0.08

IBM 0.02 0.07 -0.13 0.00 0.23

Ingersol 0.00 0.90 -0.02 0.75 -0.04

Int. Paper 0.00 0.97 0.02 0.66 -0.04

Johnson 0.10 0.56 -0.12 0.16 0.00

McGraw Hill 0.06 0.41 -0.15 0.03 0.07

Merck 0.96 0.01 -0.20 0.03 0.19

Motorola 0.03 0.09 -0.02 0.53 0.02

Olin 0.00 0.74 -0.16 0.07 0.03

Pfizer 0.37 0.17 -0.12 0.23 0.02

Raytheon 0.12 0.11 -0.08 0.10 0.08

Textron 0.02 0.38 -0.04 0.34 -0.02

United Tech. 0.01 0.38 0.01 0.78 -0.02

Average 0.12 0.31 -0.10 0.33 0.06

Standard Dev. 0.20 0.27 0.12 0.28 0.09

No. times sig.

4

8

of 38

Table 9: Coefficient estimates and inferential statistics for the ‘reverse causality’ error

correction model:

(

)

Firms t-Prob. t-Prob.

Abbott 0.11 0.00 0.08 0.41 -0.01 1

Altira 0.14 0.00 -0.09 0.31 0.00 6 1

Beam 0.03 0.93 -0.52 0.00 0.24 9 1

Bristol 0.15 0.00 -0.12 0.02 0.11 8 1

Chevron 0.06 0.37 -0.66 0.00 0.34 9 1

Coca Cola 0.11 0.00 -0.01 0.86 -0.02 7

Colgate 0.09 0.19 -0.80 0.00 0.39 7 1

Cooper 0.08 0.82 -1.05 0.00 0.50 8 1

Corning 0.00 0.99 -0.97 0.00 0.36 8 1

Crane 0.05 0.84 -0.58 0.00 0.27 8 1

Curtiss 0.00 0.99 -0.90 0.00 0.44 7 1

CVS 0.08 0.78 -0.95 0.00 0.46 9 1

Du Pont 0.02 0.96 -0.94 0.00 0.45 9 1

Eaton 0.06 0.88 -0.98 0.00 0.48 9 1

Exxon 0.07 0.03 -0.15 0.05 0.06 8 1

General Electric 0.09 0.00 -0.03 0.63 -0.02 6

Goodyear 0.25 0.51 -1.00 0.00 0.49 8 1

Honeywell 0.18 0.73 -0.74 0.00 0.35 10 1

IBM 0.09 0.86 -0.37 0.00 0.16 6 1

Ingersol 0.04 0.91 -0.98 0.00 0.48 7 1

Int. Paper 0.21 0.48 -0.89 0.00 0.43 9 1

Johnson 0.14 0.00 -0.16 0.03 0.09 7 1

McGraw Hill 0.09 0.28 -0.42 0.00 0.17 9 1

Merck 0.13 0.00 -0.02 0.66 -0.02 7 1

Motorola 0.38 0.29 -0.98 0.00 0.47 6 1

Olin 0.13 0.76 -1.02 0.00 0.50 8 1

Pfizer 0.12 0.00 -0.06 0.33 0.00 8

Raytheon 0.23 0.04 -0.46 0.00 0.17 8 1

Textron 0.09 0.75 -1.03 0.00 0.51 9 1

United Tech. 0.06 0.90 -0.63 0.00 0.30 7 1

Average 0.11 0.48 -0.58 0.11 0.27 7.60 0.87

Standard Dev. 0.08 0.40 0.39 0.23 0.20 1.65

No. times sig.

10

23

Note:

A ‘1’ in the last column indicates evidence of co-integration in the

ADF tests described in Table 2.

of 38

Table 10: Coefficient estimates and inferential statistics for the error correction model:

(

)

Firms t-Prob.

Abbott 0.01 0.47 -0.01 10

Altira 0.01 0.64 -0.02 7

Beam -0.52 0 0.24 7

Bristol -0.01 0.3 0 8

Chevron -0.23 0.02 0.09 8

Coca Cola 0.01 0.68 -0.02 7

Colgate -0.09 0.2 0.02 7

Cooper -0.86 0 0.42 6

Corning -0.94 0 0.33 8

Crane -0.46 0 0.21 10

Curtiss -0.81 0 0.39 7

CVS -0.68 0 0.32 8

Du Pont -0.92 0 0.44 8

Eaton -0.87 0 0.42 7

Exxon -0.01 0.75 -0.02 7

General Electric 0.01 0.62 -0.02 5

Goodyear -0.96 0 0.38 7

Honeywell -0.82 0 0.35 10

IBM -0.36 0 0.16 8

Ingersol -0.91 0 0.44 10

International Paper -0.96 0 0.29 8

Johnson 0 0.92 -0.02 8

McGraw Hill -0.12 0.1 0.04 8

Merck 0 0.69 -0.02 5

Motorola -0.98 0 0.35 6

Olin -1.03 0 0.48 7

Pfizer 0.02 0.25 0.01 1

Raytheon -0.14 0.39 -0.01 7

Textron -0.83 0 0.41 9

United Tech. -0.57 0 0.26 7

Average -0.47 0.2 0.2 7.37

Standard Dev. 0.41 0.29 0.19 1.77

No. times sig. 18

of 38

Table 11: Estimates from an error correction model of the error in earnings relative to retained earnings

Firms

Abbott 0.29 1.99 2.42 2.78 0.26 3.32 0.13 1.54 0.28 3.39 0.56

Altira 0.87 22.40 0.51 1.93 0.02 1.32 0.05 2.52 0.93 4.03 0.54

Beam -0.09 0.60 -1.61 -1.42 0.92 6.06 0.36 1.71 0.50 -1.47 1.17

Bristol -0.16 1.00 1.88 2.74 0.74 9.99 0.15 1.08 0.72 1.62 0.77

Chevron 0.96 24.10 0.42 1.75 0.04 2.27 -0.06 -3.12 0.94 11.10 -0.44

Coca Cola 0.12 0.72 0.25 0.59 0.91 13.50 -0.06 0.39 0.82 0.29 0.96

Colgate 0.21 1.39 1.07 1.74 0.51 5.27 0.11 0.92 0.41 1.35 0.78

Cooper 0.19 1.16 0.55 1.17 0.71 7.69 0.03 0.17 0.68 0.67 0.90

Corning -0.21 -1.43 1.70 4.96 0.79 9.00 -0.11 0.82 0.66 1.41 0.56

Crane 0.14 0.93 0.85 2.02 0.43 4.41 0.21 1.81 0.38 0.99 0.75

Curtiss -0.52 -3.72 1.48 3.08 0.72 7.70 0.47 3.71 0.69 0.98 0.78

CVS 0.47 3.38 1.39 1.62 0.40 4.24 -0.05 0.47 0.40 2.64 0.66

Du Pont 0.30 2.03 2.37 3.41 0.23 2.75 0.05 0.58 0.21 3.41 0.41

Eaton 0.82 10.70 1.01 1.81 0.04 2.01 0.02 0.87 0.80 5.72 0.37

Exxon 0.12 0.73 1.16 1.66 0.56 5.04 0.11 0.73 0.44 1.31 0.75

Gen. Electric 0.90 20.20 0.38 1.21 0.06 2.89 0.01 0.32 0.93 3.76 0.63

Goodyear -0.29 -1.85 1.32 2.72 0.75 8.87 0.33 2.29 0.68 1.03 0.84

Honeywell 0.13 0.84 1.01 1.78 0.71 8.49 0.03 0.20 0.65 1.16 0.85

IBM 0.07 0.46 1.18 2.50 0.76 10.30 -0.06 0.41 0.72 1.28 0.76

Ingersol 0.63 5.04 1.91 2.20 0.25 3.40 -0.10 -1.24 0.53 5.19 0.41

Int. Paper 0.30 1.81 -0.10 0.20 0.70 7.52 -0.04 0.28 0.72 -0.14 0.94

Johnson 0.91 16.20 0.32 1.29 0.10 3.24 -0.04 -1.33 0.94 3.64 0.66

McGraw Hill -0.18 -1.19 0.03 0.30 0.99 45.20 0.21 1.36 0.99 0.02 1.02

Merck 0.24 1.90 2.10 2.19 0.04 0.55 0.42 4.57 0.39 2.76 0.61

Motorola 0.09 0.58 1.00 1.45 0.61 5.82 0.09 0.64 0.50 1.10 0.78

Olin 0.04 0.25 1.18 2.68 0.70 6.27 -0.14 -1.04 0.51 1.23 0.58

Pfizer -0.12 0.67 5.15 6.40 0.75 5.69 -0.57 -2.79 0.42 4.62 0.16

Raytheon 0.62 4.87 0.97 1.92 0.28 3.63 -0.03 0.30 0.64 2.54 0.65

Textron 0.19 1.01 2.11 2.54 0.32 2.84 0.03 0.22 0.18 2.61 0.43

United Tech. 0.17 1.04 1.07 1.80 0.66 7.74 0.04 0.31 0.66 1.28 0.84

Average 0.24 3.93 1.17 2.03 0.50 6.90 0.05 0.62 0.61 2.32 0.66

SD 0.38 7.22 1.12 1.40 0.30 7.84 0.20 1.58 0.22 2.34 0.30

SE 0.07 1.34 0.21 0.26 0.06 1.46 0.04 0.29 0.04 0.43 0.06

LCL 0.10 1.30 0.76 1.53 0.39 4.05 -0.02 0.05 0.53 1.47 0.55

UCL 0.38 6.55 1.58 2.54 0.61 9.76 0.12 1.20 0.69 3.17 0.76

Notes

of 38

Figures

of 38

Figure 1: Time series behaviour of the Price-Earnings ratio and the earnings elasticity

of market value 1955 -2011

Panel A:

Panel B:

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

19

55

19

58

19

61

19

64

19

67

19

70

19

73

19

76

19

79

19

82

19

85

19

88

19

91

19

94

19

97

20

00

20

03

20

06

20

09

Axi

s Ti

tle

Price Earnings Ratio by Year

PE ratio

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

19

55

19

59

19

63

19

67

19

71

19

75

19

79

19

83

19

87

19

91

19

95

19

99

20

03

20

07

20

11

Earnings Elasticity of Market Value

Earnings elasticity

of 38

Figure 1 (Continued): Time series behaviour of the Price-Earnings ratio and the

earnings elasticity of market value 1955 -2011

Panel C:

Panel D:

0.00

5.00

10.00

15.00

20.00

25.00

30.00

19

55

19

58

19

61

19

64

19

67

19

70

19

73

19

76

19

79

19

82

19

85

19

88

19

91

19

94

19

97

20

00

20

03

20

06

20

09

Theta by Year

Theta

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

19

55

19

59

19

63

19

67

19

71

19

75

19

79

19

83

19

87

19

91

19

95

19

99

20

03

20

07

20

11

Rat

io

PE Ratio to Theta by Year

PE / Theta

of 38

Figure 2: Average error in published earnings after deducting dividends compared to changes

in retained earnings for 30 large US firms, 1960 – 2011.

Note: Amounts are in US$m.

earnings in firm valuation and their value relevance · page 1 of 38 earnings in firm valuation and...

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